Not -rubbing in/applying- the cream regularly will cause/allow the disease to reemerge . Because the cream was not rubbed in regularly, the disease reemerged.

"Not rubbing the cream regularly‚ the disease emerges again." Strictly speaking, the sentence is not right. The first part is a "participle phrase" showing a state or action that exists in parallel or underlying the main clause. They commonly do not have a separate noun acting as a subject, in which case the main clause's subject is also the subject of the participle phrase. Your sentence falls into this category and therein lies the problem. The main clause subject, "disease", is acting as the subject of the participle clause "Not rubbing..." which doesn't make sense since it is not the disease that rubs the cream. So you must add the subject, like "The patient not rubbing the cream regularly, the disease emerges again". It is now a phrase with its own subject and the meaning is clear. Look at these simple examples to illustrate the point. - I went to the bank. / I drove a car (to go to the bank). => I went to the bank driving my car. ("I" is the subject for both "went" and "driving") - I went to the bank (with my friend) / My friend drove a car (taking me and him to the bank) => I went to the bank, my friend driving the car. (now "driving" has its own subject) They have the essentially the same structure as your sentence. Whether you use "Rubbing..." or "Having rubbed..." is just a matter of tense. In this example both can work. "Having rubbed" more clearly indicates that (not) rubbing occurs first and as a result the diseases emerges. But in this particular example, it still makes sense even if you don't state this point so clearly.